Linear Operators: Spectral operators |
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Page 2031
... derivatives of tempered distributions as we did for distri- butions . The motivating factor for the definition is ... derivative po determines a tempered distri- bution . Suppose , for example , that po , y are both in Ø . Then an ...
... derivatives of tempered distributions as we did for distri- butions . The motivating factor for the definition is ... derivative po determines a tempered distri- bution . Suppose , for example , that po , y are both in Ø . Then an ...
Page 2042
... derivatives functions which are the restrictions of the corresponding derivatives of T ,. Thus conclusion ( ii ) of Theorem XIV.4.5 applies with n = N , p = 2 , and k arbitrarily large , to show that all derivatives of T , are ...
... derivatives functions which are the restrictions of the corresponding derivatives of T ,. Thus conclusion ( ii ) of Theorem XIV.4.5 applies with n = N , p = 2 , and k arbitrarily large , to show that all derivatives of T , are ...
Page 2447
... derivatives , mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( † ƒ ) ( x ) = exp ( a ( x ) ) f ( ( x ) ...
... derivatives , mapping the interval [ 0 , 1 ] into itself . Let be the inverse of the mapping 4. Let a ( x ) be a complex valued function with two continuous derivatives defined in [ 0 , 1 ] . Put ( † ƒ ) ( x ) = exp ( a ( x ) ) f ( ( x ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero